We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of...

Beauchêne, Li, and Li (2019) show that ambiguous persuasion leads to new interim equilibria with higher ex ante value for the Sender compared to the standard Bayesian persuasion. However, in their equilibrium the strategy of the Receiver is in general not ex ante optimal. This note, defines...

We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version of Fubini's theorem for stochastic...

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional space X, it takes values in the positive cone...

We obtain so far unproved properties of a ratio involving a class of Hermite and parabolic cylinder functions. Those ratios are shown to be strictly decreasing and bounded by universal constants. Differently to usual analytic approaches, we employ simple purely probabilistic arguments to derive...

We consider the surplus process of a life insurer who is able to buy a securitisation product to hedge mortality in a discrete time framework. Two cohorts are considered: one underlying the securitisation product and one for the portfolio of the insurer. In our main result we show that there...

We solve an infinite time-horizon bounded-variation stochastic control problem with regime switching between N states. This is motivated by the problem of a government that wants to control the country's debt-to-GDP (gross domestic product) ratio. In our formulation, the debt-to-GDP ratio...

This paper examines the stability of balanced paths of expansion or contraction in closed macroeconomic models as typical cases of homogeneous dynamical systems. Examples of known two-dimensional deterministic and stochastic models are discussed. The appendix presents the mathematical tools and...

In this paper we construct the smallest semigroup S that dominates a given family of linear Feller semigroups. The semigroup S will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong continuity properties of the semigroup envelope and show that it...

This paper studies two player stopping games in a discrete time multiple prior framework with a finite time horizon. Optimal stopping times as well as recursive formulas for the value processes of the games are derived. These results are used to characterize the set of no-arbitrage prices for a...